Mathematical breakthroughs influenced Shakespeare’s stories

Linguists proved Shakespeare wrote his plays

In the 1800s, linguist Wincenty Lutoslawski invented a method of linguistics analysis called stylometry to help certify literary authorship. Stylometrists concluded that Shakespeare wrote his plays, and likely collaborated with Christopher Marlowe for some.

Shakespeare's storytelling uses intricate, intertwining narratives

According to one professor, readers return to Shakespeare's plays, not for his storylines, but to learn how things unfold. In the process, they often use his plays to understand why humans act the way they do.

Shakespeare played a major role in the history of the sonnet

The Renaissance writer Petrarch first developed the 14-line poem with a two-part structure. Through English translations of his sonnets by Sir Thomas Wyatt in the 1500s, the form took on new life, particularly through Shakespeare. Variations on the form have continued to evolve since.

Shakespeare wrote 38 plays between 1580 and 1614

Between 1600 and 1610, he produced some of his best-known works, including “Hamlet,“ “Othello,“ “King Lear,“ and “Macbeth.“

Dozens of common phrases are attributed to Shakespeare

His clever wordsmithery infiltrated English, from “Neither rhyme nor reason” to “In my heart of hearts.” This article lists nearly two dozen of his best-known phrases.

Shakespeare's American productions have often reflected the state of the country

Shakespeare's works have been used to interpret moments in US history, from the Astor Place Riot in 1849 and Lincoln's frequent quotations of "Macbeth," to the use of Shakespeare in nationwide classrooms today.

Shakespeare was criticized in his own time

Robert Greene was a respected writer during Shakespeare’s time as an actor-playwright who famously dismissed the young upstart, accusing him of plagiarism and criticizing his ability to write blank verse.

Critic Harold Bloom believed Shakespeare invented the modern human

Yale critic Harold Bloom believed the Bard transformed the way humanity understood itself, a thesis laid out in his book "Shakespeare: The Invention of the Human."

In addition to his plays, Shakespeare wrote nearly 200 poems

Beyond his famous plays, Shakespeare penned 154 sonnets, including the well-known romantic ode “Shall I compare thee to a summer’s day?” He also wrote two long poems as well as several minor pieces.

Shakespeare’s plays were first published together in 1623 after his death

Most of his plays were written for the stage, so it took his admirers to compile the play texts posthumously in 1623. This became the famous “First Folio,” the basis of Shakespeare’s literary posterity.

10 Shakespeare authorship theories

Although William Shakespeare is widely considered to be the authentic author of the plays attributed to him, there are still dozens of theories suggesting that others are responsible for the classic works. Was it actually his contemporary, Christopher Marlowe? Or maybe his wife, Anne Hathaway? This list explains the 10 most popular theories that have been proposed, much to more than a few Shakespeare scholars' chagrin.

Documented proof of Shakespeare’s life

Birth in 1564 in the small town of Stratford-upon-Avon; marriage to Anne Hathaway in 1582; and the appearance of his first born (1583) and first printed play (1594): If you’ve ever doubted the Bard’s existence, here are his life’s milestones backed by historical documents.

Mathematicians often solve problems using wordless mental processes

It's a common technique among expert mathematicians, where thinkers rely on intuition, blurry perceptions and subconscious work—no writing, no formulas. The state is distinct from daydreaming, and often relies on sudden illuminations stemming from extended periods of subconscious reflection.

How Shakespeare changed the sonnet

A sonnet is a rigid poetic form from the Renaissance, featuring 14 lines, a consistent meter (or beat) and rhyme scheme, and a noticeable thematic shift known as a "volta." Shakespeare popularized a form featuring three four-line stanzas and a rhyming couplet, departing from the Petrarchan two-part structure of eight- and six-line stanzas.

The Ishango bone suggests mathematics was born about 20,000 years ago

Ancient civilizations developed mathematical systems for various purposes, including the Egyptians for the construction of the pyramids and the Ancient Greeks for logical reasoning in theorems. However, these systems were predated by the Ishango bone—found in the Democratic Republic of the Congo—whose notches suggest a base ten system, prime numbers, and simple mathematical operations.

Enlightenment ideals of reason informed the foundation of the Revolution

From the 17th to 19th centuries, an intellectual movement took place in Europe and its colonies that emphasized reason over authority. Following the Scientific Revolution, thinkers like Descartes, Kant, and Locke sought to explain the world in rational—rather than religious—terms. The movement caused a paradigm shift in how societies are organized and how people perceive themselves.

Some doubt Shakespeare is who scholars say he is

Major contemporaries of Shakespeare have been proposed as the real writer of his plays and poems, including Anne Hathaway, Ben Jonson, and Sir Walter Raleigh.

The magic angle to skip a spinning stone is 20 degrees

The traditional shoreside activity—reputedly practiced by luminaries Shakespeare and Homer—can be broken down into its bare physics, from hydrodynamics and momentum to gravity.

A list of nine quirky literary adaptations of Shakespeare's life and works

Although surprisingly little is known about the actual man, William Shakespeare holds an unrivalled place in English letters. His characters, from Hamlet to Hermione, have inspired countless imitators, responses, and caricatures, and this list gathers a few of the best for the modern reader, including Richard Adams' adaptation of King Lear through a story about dogs.

Galileo’s discovery of Jupiter’s moons led to multiple scientific advancements

Beyond challenging Earth-centric views upon their discovery in 1610, the Galilean moons were also later analyzed to contribute to early astrometry and astronomical interferometry. Measurements of eclipses were also used to estimate the speed of light.

Early 20th-century debates about horses with 'paranormal mathematical abilities' helped shape modern approaches to psychological research.

Disillusioned mid-century playwrights, such as Samuel Beckett and Eugène Ionesco, brought existentialist ideas to the stage through the Theater of the Absurd.

The best Shakespeare plays, ranked

The Guardian worked through the Bard's plays, from "A Midsummer Night's Dream" to "The Winter's Tale," evaluating what distinguishes the mediocre from the truly excellent.

Shakespeare wrote in an early form of Modern English—not Old English

Old, Middle, and Modern English are three distinct language eras. A speaker of Modern English wouldn’t be able to understand Old or Middle English.

Four astronomical discoveries from ancient Greece

Modern astronomy relies on making discoveries without being present on the planets, stars, galaxies, and other objects studied. Imagine the difficulty the ancient Greeks had studying them without computers and telescopes. Yet somehow they calculated precise measurements of planetary distances, sizes, and more. Read this page to learn more about early triumphs in astronomical science.

The sophisticated math jokes of 'The Simpsons'

"The Simpsons" has always been a slyly sophisticated show and has featured more than a few references to complex mathematical concepts. That's largely due to its writers' room, which has featured more than one writer who studied math before transitioning to comedy.

One of the first mechanical calculators—the Pascaline—was built in the 1640s by French mathematician Blaise Pascal to help his father, who worked as a tax collector.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

Shakespeare included a reference to toasting in ‘The Merry Wives of Windsor’

At one point in the 1602 play, the character Falstaff calls for a quart of wine, asking for toast to be placed in it, as was customary at the time.

Playwright George Bernard Shaw believed Shakespeare was overrated

Shaw was one of the titans of 20th-century British drama—responsible for "Pygmalion," "Arms and the Man," and more—and a persistent critic of the Bard, whom he believed had been unnecessarily praised to the point of "Bardolatry." Over time, his opinion softened; at one point, Shaw even reworked Shakespeare's "Cymbeline."

Trade and conquest carried chess into Europe by the 11th century

After spreading through Persia, chess traveled along Islamic military and trade routes into North Africa and Moorish Spain by the 10th century. By the 11th century, it had taken root across much of Europe, flourishing in courts and monasteries.

'Romeo and Juliet' was based on a preexisting narrative poem

Arthur Brooke's "The Tragical History of Romeus and Juliet" was first published in 1562 and shares many details with Shakespeare's "Romeo and Juliet." Shakespeare wasn't alone in his borrowing; Brooke's poem was based on other earlier Italian stories. None of this writing was considered fan fiction—copyright law didn't exist, and stories were regularly cribbed from preexisting sources.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

How a brain injury created a mathematical mind

In 2002, two men savagely attacked Jason Padgett outside a karaoke bar, leaving him with a severe concussion--and turning Padgett into a mathematical genius.

‘Blank verse’ is an unrhymed poetic form with a consistent meter common in epics

Shakespeare’s plays are primarily written in blank verse, a consistent meter without any rhyme scheme. The mode is common in epic poems like Homer’s Iliad or John Milton’s “Paradise Lost,” though the specific meters vary.

The history of the 10 axioms of Zermelo–Fraenkel set theory with choice, regarded as the most universal foundations of math

Like postulates in geometry—accepted truths that form the logical building blocks for formal proofs of more complex theorems—axioms cannot be proven, but set the underlying logic and rules for systems. The ZFC axioms resulted from painstaking work to identify the underlying rules of mathematics and are built on the premise of sets, or well-defined collections of elements.

The Middle Ages produced inventions that still affect our lives today, like coffee houses and improved agricultural techniques.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

Critics often use the word ‘Shakespearean’ to describe a dramatic story

Calling something “Shakespearean” often denotes a high-quality work of art or a story that recalls one of the Bard’s plays.

One '$64,000 Question' winner went from police officer to Shakespearean scholar overnight

Redmond O’Hanlon was a police officer living on Staten Island, New York, when he competed on “The $64,000 Question.” His knowledge of Shakespeare earned him $16,000, which was four times his annual salary. After appearing on the show, he became a minor celebrity, and created a Shakespeare-themed set of playing cards and established the O'Hanlon Shakespeare Service, a consultancy on the Bard, all while continuing to work for the NYPD.

Shakespeare’s use of verse and prose signifies important characteristics

Structured verse signals formality, often used by high-ranking characters; in contrast, unstructured prose is typically used in informal, more witty situations by lower-status characters.

Nine Shakespeare paintings by pre-Raphaelite John Everett Millais

In the 19th century, pre-Raphaelites like Millais sought to showcase life and nature honestly, using common references like the Bible, ordinary people and Shakespeare. Explore some of Millais' better known paintings inspired by the Bard here, including his world-renowned "Ophelia."

The role stories play in mass economic trends like bitcoin, crashes

Economics is dominated by numbers, but stories play a huge role in the emotional shifts seen within macroeconomic trends. For example, bitcoin is not just a cost-benefit winner, but a compelling tale of decentralization and independence. This is a 20-minute summary of Nobel prize-winning economist Robert Shiller's "Narrative Economics."

In 2000, the Clay Mathematics Institute placed million-dollar bounties on seven unsolved problems in mathematics—the Millennium Prize Problems—in the hopes of spurring solutions.

Bear-baiting was another form of entertainment during Shakespeare’s time

We tend to think of Shakespeare’s audiences as prim and proper, but the Bard’s shows were just another form of amusement, viewed by commoners as entertainment not unlike the animal blood sports that were similarly popular during the time period.

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

Science is rarely a linear progression of understanding

Particularly at the frontiers, investigations conducted based on established knowledge can provide unexpected results. This opens the door to revising existing models, inspiring new lines of research, and ultimately leading to better future comprehension. For instance, experiments on the speed of light and the expansion of the universe yielded then-confusing data that led to revolutionary insights.

Money—not land—became Europe’s key economic driver in the Middle Age

During the medieval commercial revolution, money gradually replaced land as the primary economic commodity. Expanding trade, markets, and finance transformed Europe’s economy—laying foundations, historians argue, that were essential for the later Industrial Revolution.

A medievalist explains how romantic love emerged as a cultural concept

Many long-form stories written in English were originally considered "romances," a term derived from the Old French word for "the speech of the people." But changes in medieval culture, triggered by a number of 12th-century church reforms, led to a new interest in what we now consider romantic love, including a new view of marriage as a pursuit of love rather than a transaction. Those new perspectives were then reflected in the period's popular stories, including stories in Chaucer's "Canterbury Tales."

No, Shakespeare didn't write the Bible

Some believe Shakespeare helped write the King James Bible—and left his name hidden in Psalm 46. The evidence seems uncanny… but the truth is much less dramatic.